CN104309437B - The method for designing of vehicle air suspension non-linear rigidity real-time optimistic control - Google Patents

Abstract

The present invention relates to the method for designing of vehicle air suspension non-linear rigidity real-time optimistic control, belong to vehicle air suspension technical field, it is characterised in that：According to the nonlinear stiffness characteristic of vehicle air spring, and the real-time Optimal damping ratio of suspension under vehicle current running state, by analytical calculation, obtain the real-time Optimal Stiffness value and the relation between height of vehicle air suspension, by controlling the height of air spring, the real-time control to air suspension Optimal Stiffness is realized.Simply and reliably vehicle air suspension non-linear rigidity real-time optimistic control can be designed using the present invention, and design and testing expenses can be reduced, improve vehicle ride performance and riding comfort.

Description

Design method for real-time optimal control of nonlinear stiffness of vehicle air suspension

technical field

The invention relates to a vehicle air suspension, in particular to a design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension.

Background technique

The core component of the air suspension is the air spring, whose principle is to use the compressibility of the gas to realize the elastic effect, thereby improving the ride comfort and ride comfort of the vehicle. According to the information obtained, due to the restriction of the nonlinear elasticity of the air spring, the real-time optimal control of the nonlinear stiffness of the vehicle air suspension has not been given a simple and reliable design method at home and abroad. High degree of real-time control of the optimal stiffness of the air suspension. Most of them use methods such as filling and releasing gases of different pressures to the rubber airbags, adding additional air chambers, and adjusting the opening of the orifice to realize real-time control of the stiffness of the air suspension. With the rapid development of the vehicle industry, the current design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension cannot meet the design requirements of vehicle development and ride comfort. Therefore, it is necessary to establish a simple and reliable design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension, that is, according to the nonlinear stiffness characteristics of the vehicle air spring and the real-time optimal damping ratio of the suspension under the current driving state of the vehicle , through analysis and calculation, the real-time optimal stiffness value of the vehicle air suspension and the relationship with the height are obtained. By controlling the height of the air spring, the real-time control of the optimal stiffness of the air suspension is realized, and the ride comfort and performance of the vehicle are further improved. ride comfort.

Contents of the invention

In view of the above-mentioned defects in the prior art, the technical problem to be solved by the present invention is to provide a simple and reliable design method for real-time optimal control of the nonlinear stiffness of the vehicle air suspension.

In order to solve the above-mentioned technical problems, the design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension provided by the present invention, its design flow chart is shown in Figure 1, and the specific steps for implementing the technical solution are as follows:

(1) Identification of nonlinear stiffness characteristic parameters of air spring:

A: Use vibration testing equipment to measure and collect the vertical vibration acceleration signal of the axle and the vertical vibration acceleration signal of the vehicle body at the center of the installation position of the single-wheel air suspension of the vehicle under a certain driving condition. The time length for collecting the vibration signal is { 0,T}={[0,t ₁ ]+[t ₁ ,T]}, where the vibration signal of the previous time period [0,t ₁ ] is used for the identification of the nonlinear stiffness characteristic parameters of the air spring, and the latter The vibration signal of the time period [t ₁ , T] is used for the simulation verification of the identification results of the nonlinear stiffness characteristic parameters;

B: According to the nonlinear stiffness characteristics of the air spring, construct an odd power polynomial F _s =k _s1 z+k _s3 z ³ , where F _s is the nonlinear elastic force of the air spring expressed by the odd power polynomial, k _s1 and k _s3 are polynomial parameters to be identified;

C: According to the sprung mass m ₂ of the vehicle's single-wheel air suspension, the nonlinear stiffness characteristic parameters k _s1 and k _s3 of the air spring to be identified, and the damping coefficient C _d of the shock absorber, a single-degree-of-freedom 1/4 vehicle vibration model is constructed ;

D: According to the air spring nonlinear elastic force odd power polynomial constructed in step B, and the single degree of freedom 1/4 vehicle vibration model constructed in step C, use Matlab/Simulink simulation software to establish a vehicle nonlinear vibration system The simulation model takes the axle vertical vibration acceleration signal measured in the previous time period [0,t ₁ ] as the input signal, and simulates the root mean square value of the vertical vibration weighted acceleration of the vehicle body. The weighted value is:

E: Taking the nonlinear stiffness characteristic parameters k _s1 and k _s3 of the air spring as identification variables, using the root mean square value of weighted acceleration of the vertical vibration of the vehicle body obtained by simulation in the time period [0,t ₁ ] The root mean square value of the weighted acceleration of the vertical vibration of the vehicle body measured in the test Establish the objective function J _min of the nonlinear stiffness identification of the air spring, namely:

F: According to the identification objective function of the nonlinear stiffness of the air spring, use the optimization algorithm to find the minimum value of the parameter identification objective function. At this time, the corresponding optimization variable is the nonlinear stiffness characteristic parameter of the air spring obtained from the identification, namely k _s1 , k _s3 ;

G: According to the air spring nonlinear elastic force odd power polynomial constructed in step B, the single-degree-of-freedom 1/4 vehicle vibration model constructed in step C, and the nonlinear stiffness of the air spring identified in step F Characteristic parameters k _s1 , k _s3 , using the axle vertical vibration acceleration signal measured in the time period [t ₁ , T] as the input signal, simulate and calculate the weighted acceleration value of the vertical vibration of the vehicle body, and compare it with that in the time period The measured vertical vibration weighted acceleration values of the vehicle body are compared to verify the identification results of the nonlinear stiffness of the air spring;

( ₂ ) Determination of the real-time optimal damping ratio ξ0 of the vehicle:

I: Use the acceleration sensor to measure the vertical vibration acceleration of the vehicle body under the current driving state Use the height sensor to measure the vertical height h ₂ of the vehicle body from the center of the installation position of the upper end point of the air suspension to the ground under the current driving state of the vehicle, and the vertical height h ₁ of the axle from the center of the installation position of the lower end point to the ground; use the speed sensor to measure the vehicle The driving speed v under the current driving state;

II: According to the natural height h ₀ of the air spring of the vehicle, and the vertical height h ₂ of the vehicle body determined in step I, and the vertical height h ₁ of the axle, determine the relative displacement between the vertical vibration of the vehicle body and the vertical vibration of the wheels under the current driving state of the vehicle, namely z=|h ₂ -h ₁ -h ₀ |;

III: According to the air spring nonlinear stiffness characteristic parameters k _s1 , k _s3 obtained in step (1), and the relative displacement z between the vertical vibration of the vehicle body and the vertical vibration of the wheel determined in step II, determine the vehicle's current motion state Air suspension stiffness K ₂ , namely:

K ₂ =k _s1 +3k _s3 z ² ;

IV: According to the sprung mass m ₂ of the single-wheel air suspension of the vehicle, the damping coefficient C _d of the shock absorber, the installation angle α of the shock absorber, the lever ratio i, and the K ₂ determined in step III, determine the current vehicle air suspension Frame system damping ratio ξ, namely:

V: According to the sprung mass m ₂ of the vehicle's single-wheel air suspension, the unsprung mass m ₁ , and the tire stiffness K _t , the vertical vibration acceleration of the vehicle body determined in step I The vehicle speed v, the air suspension stiffness K ₂ determined in the current state of motion of the vehicle determined in step III, and the damping ratio ξ of the current vehicle air suspension system determined in step IV, determine the power spectral density G of the vehicle's current road surface _q (n ₀ ), that is:

In the formula, n ₀ =0.1m ^-1 , which is the reference spatial frequency;

VI: According to the power spectral density G _q (n ₀ ) of the vehicle’s running road surface determined in step V, use the relationship between the dynamic deflection probability distribution and the standard deviation of the suspension spring at different driving speeds to determine the suspension Mounting limit travel [f _dx ], that is:

VII: According to the sprung mass m ₂ of the vehicle's single-wheel air suspension, the unsprung mass m ₁ , the tire stiffness K _t , the current vehicle speed v determined in step I, and the current vehicle speed v determined in step III The air suspension stiffness K ₂ , the power spectral density G _q (n ₀ ) of the vehicle running road surface determined in the V step, and the suspension dynamic limit travel [f _dx ] determined in the VI step, determine the real-time optimal damping of the vehicle than ξ ₀ , namely:

In the formula, n ₀ =0.1m ^-1 , which is the reference spatial frequency;

(3) Determination of the real-time optimal stiffness K of the air suspension under the current driving state of the vehicle:

According to the sprung mass m ₂ of the vehicle's single-wheel air suspension, the damping coefficient C _d of the shock absorber, the installation angle α of the shock absorber, the lever ratio i, and the real-time optimal damping ratio ξ of the vehicle determined in step (2) ₀ , to determine the real-time optimal stiffness K of the air suspension under the current driving state of the vehicle, namely:

(4) The design of the real-time optimal height control quantity of the nonlinear stiffness of the air suspension:

According to the air spring nonlinear stiffness characteristic parameters k _s1 and k _s3 obtained in step (1), and the real-time optimal stiffness K of the vehicle air suspension under the current driving state determined in step (3), the air The real-time optimal height control amount Δh of the spring is designed, namely:

The present invention has the advantage over prior art:

Previously, a simple and reliable design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension has not been given, and no real-time control of the optimal stiffness of the air suspension by controlling the height of the air spring has been proposed. Most of them use methods such as filling and releasing gases of different pressures into the rubber airbags, adding additional air chambers, and adjusting the opening of the orifice to realize real-time control of the stiffness of the air suspension, which cannot meet the design requirements of vehicle development and vehicle ride comfort. The design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension according to the present invention, that is, according to the nonlinear stiffness characteristics of the vehicle air spring and the real-time optimal damping ratio of the suspension under the current driving state of the vehicle, through analysis and calculation, the vehicle air suspension can be obtained. The relationship between the real-time optimal stiffness value of the suspension and its height. By controlling the height of the air spring, the real-time control of the optimal stiffness of the air suspension can be realized. At the same time, the test and design costs can be reduced, and the ride comfort and ride quality of the vehicle can be improved. comfort.

Description of drawings

In order to better understand the present invention, the following will be further described in conjunction with the accompanying drawings.

Fig. 1 is a flow chart of the design process of the real-time optimal control of the nonlinear stiffness of the vehicle air spring;

Fig. 2 is the vertical vibration acceleration signal of the vehicle axle at the center of the installation position of the vehicle single-wheel air suspension measured in the embodiment test;

Fig. 3 is the vertical vibration acceleration signal of the vehicle body at the center of the installation position of the single-wheel air suspension of the vehicle measured in the embodiment test;

Fig. 4 is embodiment single degree of freedom 1/4 vehicle vibration model;

Fig. 5 is the Simulink simulation model of embodiment vehicle nonlinear vibration system;

Fig. 6 is a schematic diagram of the installation position of the sensor of the embodiment;

Fig. 7 is the relationship curve of the nonlinear stiffness of the embodiment air suspension with the variation of air spring height;

Fig. 8 is the variation curve of embodiment air spring height variation with vehicle speed;

Fig. 9 is a variation curve of the variation of the height of the air spring according to the road conditions of the embodiment.

detailed description

The present invention will be further described in detail through an embodiment below.

Example: The sprung mass m ₂ =400kg of the single-wheel air suspension of a vehicle, the unsprung mass m ₁ =40kg, the natural height h ₀ of the air spring =0.24m, and the damping coefficient C _d of the shock absorber =2723N.s/ m, shock absorber installation angle α=10°, lever ratio i=0.9, tire stiffness K _t =260000N/m, and the vehicle is running at a speed of 80km/h on the expressway. The real-time optimal height control quantity of the vehicle's air suspension nonlinear stiffness is designed.

The design method for the real-time optimal control of the nonlinear stiffness of the vehicle air suspension provided by the embodiment of the present invention, the specific steps are as follows:

(1) Identification of nonlinear stiffness of air spring:

A: Use the vibration test equipment to measure and collect the vertical vibration acceleration signal of the axle and the vertical vibration acceleration signal of the vehicle body at the center of the installation position of the single-wheel air suspension of the vehicle when the vehicle is running at a speed of 80km/h on the expressway. As shown in Figure 2 and Figure 3, the time length for collecting vibration signals is 120s, where the vibration signals of the previous period [0, 60s] are used to identify the nonlinear stiffness of the air spring, and the vibration signals of the latter period [60s, 120s] The vibration signal is used for the simulation verification of the nonlinear stiffness identification results;

B: According to the nonlinear stiffness characteristics of the air spring, construct an odd power polynomial F _s =k _s1 z+k _s3 z ³ , where F _s is the nonlinear elastic force of the air spring expressed by the odd power polynomial, k _s1 and k _s3 are polynomial parameters to be identified;

C: According to the sprung mass m ₂ =400kg of the single-wheel air suspension of the vehicle, the nonlinear stiffness characteristic parameters k _s1 and k _s3 of the air spring to be identified, and the damping coefficient C _d of the shock absorber =2723N.s/m, the construction unit 1/4 degree of freedom vehicle vibration model, as shown in Figure 4;

D: According to the air spring nonlinear elastic force odd power polynomial constructed in step B, and the single degree of freedom 1/4 vehicle vibration model constructed in step C, use Matlab/Simulink simulation software to establish a vehicle nonlinear vibration system The simulation model, as shown in Figure 5, takes the vertical vibration acceleration signal of the vehicle axle measured in the previous time period [0, 60s] as the input signal, and simulates the root mean square value of the vertical vibration weighted acceleration of the vehicle body, where, The weighted values at different frequencies are:

E: Take the nonlinear stiffness characteristic parameters k _s1 and k _s3 of the air spring as the identification variables, and use the root mean square value of the weighted acceleration of the vertical vibration of the vehicle body obtained by simulation in the time period [0,60s] The root mean square value of the weighted acceleration of the vertical vibration of the vehicle body measured in the test Establish the objective function J _min of the nonlinear stiffness identification of the air spring, namely:

F: According to the identification objective function of the nonlinear stiffness of the air spring, use the optimization algorithm to find the minimum value of the parameter identification objective function. At this time, the corresponding optimization variable is the nonlinear stiffness characteristic parameter of the air spring obtained from the identification, namely k _s1 =495.2N/m, k _s3 =6.08×10 ⁶ N/m ³ ;

G: According to the air spring nonlinear elastic force odd power polynomial constructed in step B, the single-degree-of-freedom 1/4 vehicle vibration model constructed in step C, and the nonlinear stiffness of the air spring identified in step F Characteristic parameters k _s1 = 495.2N/m, k _s3 = 6.08×10 ⁶ N/m ³ , take the vertical vibration acceleration signal of the vehicle axle measured in the time period [60s, 120s] as the input signal, and weight the vertical vibration of the vehicle body The acceleration value is simulated and calculated, and compared with the weighted acceleration value of the vertical vibration of the vehicle body measured in this period of time, the identification results of the nonlinear stiffness of the air spring are verified. Among them, in the latter period of time [60s, 120s] The simulated value of the vibration weighted acceleration of the vehicle body is 0.416m/s ² , and the experimental value is 0.419m/s ² , and the deviation between the two is only 0.003m/s ² , indicating that the established identification method for the nonlinear stiffness of the air spring is correct. of;

( ₂ ) Determination of the real-time optimal damping ratio ξ0 of the vehicle:

I: Use the acceleration sensor to measure the vertical vibration acceleration of the vehicle body under the current driving state Use the height sensor to measure the vertical height h ₂ of the vehicle body from the center of the installation position of the upper end point of the air suspension to the ground under the current driving state of the vehicle = 0.59m, and the vertical height h ₁ of the axle from the center of the installation position of the lower end point to the ground = 0.31m; Utilize the speed sensor to measure the driving speed v=80km/h under the current driving state of the vehicle; wherein, the schematic diagram of the installation position of the sensor is shown in Figure 6;

II: According to the natural height h ₀ of the vehicle air spring = 0.24m, and the vertical height of the vehicle body h ₂ = 0.59m determined in step I, the vertical height of the axle h ₁ = 0.31m, determine the vertical vibration of the vehicle body under the current driving state The relative displacement with the vertical vibration of the wheel, that is, z=|h ₂ -h ₁ -h ₀ |=0.04m;

III: Based on the air spring nonlinear stiffness characteristic parameters k _s1 = 495.2N/m, k _s3 = 6.08×10 ⁶ N/m ³ identified in step (1), and the vertical vibration and The relative displacement z=0.04m of the vertical vibration of the wheel determines the stiffness K ₂ of the air suspension under the current state of motion of the vehicle, namely:

K ₂ =K _s1 +3K _s3 z ² =29679N/m;

IV: According to the sprung mass m ₂ of the single-wheel air suspension of the vehicle = 400kg, the damping coefficient of the shock absorber C _d = 2723N.s/m, the installation angle of the shock absorber α = 10°, the lever ratio i = 0.9, and III K ₂ determined in the step = 29679N/m, determine the damping ratio ξ of the air suspension system of the current vehicle, namely:

V: According to the sprung mass m ₂ =400kg of the vehicle's single-wheel air suspension, the unsprung mass m ₁ =40kg, and the tire stiffness K _t =260000N/m, the vertical vibration acceleration of the vehicle body determined in step I Vehicle speed v=80km/h, air suspension stiffness K ₂ in the current vehicle motion state determined in step III=29679N/m, and damping ratio ξ of the current vehicle air suspension system determined in step IV=0.31 , to determine the power spectral density G _q (n ₀ ) of the vehicle’s current road surface, namely:

In the formula, n ₀ =0.1m ^-1 , which is the reference spatial frequency;

VI: According to the power spectral density G _q (n ₀ )=3.33×10 ^-5 m ³ of the road surface determined in step V, using the relationship between the dynamic deflection probability distribution and the standard deviation of the suspension spring at different driving speeds, Determine the suspension dynamic limit stroke [f _dx ] under the current state of motion of the vehicle, namely: [f _dx ]=0.05m;

VII: According to the sprung mass m ₂ =400kg of the vehicle's single-wheel air suspension, the unsprung mass m ₁ =40kg, and the tire stiffness

K _t =260000N/m, the current vehicle speed v=80km/h determined in step I, the stiffness of the air suspension under the current motion state of the vehicle determined in step III K ₂ =29679N/m, determined in step V Power Spectral Density of Vehicle Driving Road

G _q (n ₀ )＝3.33×10 ^-5 m ³ , and the suspension dynamic limit stroke [f _dx ]＝0.05m determined in step VI, determine the optimal damping ratio ξ ₀ in real time when the vehicle is running, namely: ξ ₀ = 0.18;

(3) Determination of the real-time optimal stiffness K of the air suspension under the current driving state of the vehicle:

According to the sprung mass m ₂ of the single-wheel air suspension of the vehicle = 400kg, the damping coefficient C _d of the shock absorber = 2723N.s/m, the installation angle of the shock absorber α = 10°, the lever ratio i = 0.9, and the steps (2 ) to determine the real-time optimal damping ratio ξ ₀ =0.18 of the vehicle running, and determine the real-time optimal stiffness K of the air suspension under the current driving state of the vehicle, namely:

(4) The design of the real-time optimal height control quantity of the nonlinear stiffness of the air suspension:

According to the air spring nonlinear stiffness characteristic parameters k _s1 = 495.2N/m, k _s3 = 6.08×10 ⁶ N/m ³ identified in step (1), and the current driving state determined in step (3), The real-time optimal stiffness of the air suspension of the vehicle is K=88269N/m, and the real-time optimal height control value Δh of the air spring is designed, namely:

Among them, the relationship curve of the nonlinear stiffness of the air suspension of the vehicle with the change of the air spring height is shown in Figure 7, the change curve of the air spring height with the vehicle speed is shown in Figure 8, and the change of the air spring height with the change of road conditions The curve is shown in Figure 9.

Claims (1)

1. the method for designing of vehicle air suspension non-linear rigidity real-time optimistic control, its specific design step is as follows：

(1) identification of air spring nonlinear stiffness characteristic parameter：

A：Using vibration test equipment, the vehicle single-wheel air suspension installation position under certain given travel operating mode is measured and collected The vehicle bridge vertical vibration acceleration signal and bouncing of automobile body acceleration signal of center are put, the time for gathering vibration signal is long It is { 0, T }={ [0, t to spend₁]+[t₁, T] }, wherein, previous time period [0, t₁] vibration signal be used for air spring it is non-linear just Spend the identification of characterisitic parameter, latter time period [t₁, T] vibration signal be used for nonlinear stiffness characteristic parameter identification result Simulating, verifying；

B：According to the nonlinear stiffness characteristic of air spring, an odd power multinomial F is built_s=k_s1z+k_s3z³, wherein, F_sFor With the nonlinear elasticity power of the air spring represented by odd power multinomial, k_s1And k_s3It is polynomial parameter to be identified；

C：According to the sprung mass m of vehicle single-wheel air suspension₂, air spring nonlinear stiffness characteristic parameter k to be identified_s1, k_s3, shock absorber damping C_d, build the vehicle vibration model of single-degree-of-freedom 1/4；

D：According to air spring nonlinear elasticity power odd power multinomial constructed in step B, and list constructed in step C The vehicle vibration model of the free degree 1/4, using Matlab/Simulink simulation softwares, sets up the emulation of vehicle non-linear vibrating system Model, with previous time period [0, t₁] measured by vehicle bridge vertical vibration acceleration signal be input signal, vehicle body is hung down Straight vibration root mean square of weighed acceleration is emulated, wherein, weighted value at different frequencies is：

$w_k\left(f_i\right)=\left\{\begin{array}{cc}0.5,& f_i\∈\[0.5,2\]Hz\\ f_i/4,& f_i\∈(2,4\]Hz\\ 1,& f_i\∈(4,12.5\]Hz\\ 12.5/f_i,& f_i\∈(12.5,80\]Hz\end{array}\right.;$

E：With the nonlinear stiffness characteristic parameter k of air spring_s1, k_s3As identification variable, using [0, t₁] time period emulation Resulting bouncing of automobile body root mean square of weighed accelerationAdd with the bouncing of automobile body weighting measured by experiment Speed root-mean-square valueSet up the object function J of air spring non-linear rigidity identification_min, i.e.,：

$J_{\min }={({\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_s\_sim}-{\mathrm{\σ}}_{{\stackrel{\·\·}{z}}_s\_test})}^2;$

F：Identification object function according to air spring non-linear rigidity, parameter identification object function is sought most using optimized algorithm Small value, now corresponding optimized variable is the nonlinear stiffness characteristic parameter of the air spring obtained by identification, i.e. k_s1, k_s3；

G：According to air spring nonlinear elasticity power odd power multinomial constructed in step B, in step C it is constructed it is single from By spending 1/4 vehicle vibration model, and the nonlinear stiffness characteristic parameter k that resulting air spring is recognized in F-step_s1, k_s3, With [t₁, T] the vehicle bridge vertical vibration acceleration signal measured by the time period is input signal, vertical vibration weighting to vehicle body plus Velocity amplitude carries out simulation calculation, and is compared with measured bouncing of automobile body weighted acceleration value within the time period, Identification result to air spring non-linear rigidity is verified；

(2) vehicle travels real-time Optimal damping ratio ξ₀Determination：

I：The bouncing of automobile body acceleration under vehicle current running state is measured using acceleration transducerPassed using height Sensor measures vehicle body vertical height h of the air suspension upper extreme point installation site center to ground under vehicle current running state₂, Vehicle bridge vertical height h of the lower extreme point installation site center to ground₁；Vehicle current running state is measured using velocity sensor Under travel speed v；

II：Natural height h according to vehicle air spring₀, and identified vehicle body vertical height h in I steps₂, vehicle bridge is vertically high Degree h₁, determine the relative displacement of vehicle current running state under body vertical vibration and analysis of wheel vertical vibration, i.e. z=| h₂-h₁-h₀ |；

III：According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1, k_s3, and institute in II steps The bouncing of automobile body of determination and the relative displacement z of analysis of wheel vertical vibration, determine the air suspension under vehicle current motion state Stiffness K₂, i.e.,：

K₂=k_s1+3k_s3z²；

IV：According to the sprung mass m of vehicle single-wheel air suspension₂, shock absorber damping C_d, shock absorber setting angle α, lever Than identified K in i, and III steps₂, determine Current vehicle airsuspension system damping ratio ξ, i.e.,：

$\mathrm{\ξ}=\frac{C_d{i}^2{\cos }^2\mathrm{\α}}{2\sqrt{K_2{m}_2}};$

V：According to the sprung mass m of vehicle single-wheel air suspension₂, unsprung mass m₁, tire stiffness K_t, identified car in I steps Body vertical vibration accelerationAir in Vehicle Speed v, III step under identified vehicle current motion state hangs Frame stiffness K₂, and identified Current vehicle airsuspension system damping ratio ξ in IV steps, determine vehicle current driving road surface work( Rate spectrum density G_q(n₀), i.e.,：

$G_q\left(n_0\right)=\frac{{\mathrm{\ξr}}_m{{\stackrel{\·\·}{z}}_2}^2}{4{\mathrm{\π}}^5{f}_0^3{n}_0^{2}v(1+r_m+4r_m{r}_k{\mathrm{\ξ}}^2)};$

In formula,N0=0.1m-¹, it is reference frequency；

VI：According to identified vehicle running surface power spectral density G in V steps_q(n₀), using vehicle in different travel speeds Lower suspension dynamic spring deflection probability distribution and the relation of standard deviation, determine the dynamic stroke-limit of suspension under vehicle current motion state [f_dx], i.e.,：

$\&lsqb;f_{dx}\&rsqb;=\left\{\begin{array}{cc}0.03,& 0\&le;G_q\left(n_0\right)\&le;32\&times;{10}^{-6}\\ 0.05,& 32\&times;{10}^{-6}<G_q\left(n_0\right)\&le;128\&times;{10}^{-6}\\ 0.07,& 128\&times;{10}^{-6}<G_q\left(n_0\right)\&le;512\&times;{10}^{-6}\\ 0.09,& 512\&times;{10}^{-6}<G_q\left(n_0\right)\&le;2048\&times;{10}^{-6}\\ 0.135,& G_q\left(n_0\right)>2048\&times;{10}^{-6}\end{array}\right.;$

VII：According to the sprung mass m of vehicle single-wheel air suspension₂, unsprung mass m₁, tire stiffness K_t, it is identified in I steps Air suspension stiffness K under the vehicle current motion state determined in vehicle current driving speed v, III step₂, in V steps really Fixed vehicle running surface power spectral density G_q(n₀), and the dynamic stroke-limit [f of identified suspension in VI steps_dx], determine car The real-time Optimal damping ratio ξ of traveling₀, i.e.,：

${\mathrm{\&xi;}}_0=\left\{\begin{array}{cc}\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}},& 9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2}\&le;\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}}\\ 9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2},& \frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}}<9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2}\&le;\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}+\frac{r_m{r}_k-2-2r_m}{{(1+r_m)}^2}}\\ \frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}+\frac{r_m{r}_k-2-2r_m}{{(1+r_m)}^2}},& 9{\mathrm{\&pi;G}}_q\left(n_0\right)n_0^{2}v\frac{1+r_m}{4f_0{r}_m{\&lsqb;f_{dx}\&rsqb;}^2}\&GreaterEqual;\frac{1}{2}\sqrt{\frac{1+r_m}{r_m{r}_k}+\frac{r_m{r}_k-2-2r_m}{{(1+r_m)}^2}}\end{array}\right.;$

In formula,n₀=0.1m^-1, it is reference frequency；

(3) under vehicle current running state the real-time Optimal Stiffness K of air suspension determination：

According to the sprung mass m of vehicle single-wheel air suspension₂, shock absorber damping C_d, shock absorber setting angle α, lever ratio i, And identified vehicle travels real-time Optimal damping ratio ξ in step (2)₀, determine air suspension under vehicle current running state Real-time Optimal Stiffness K, i.e.,：

$K=\frac{{C_d}^2{i}^4{\cos }^4\mathrm{\&alpha;}}{4{\mathrm{\&xi;}}_0^2{m}_2};$

(4) design of the real-time optimal height controlled quentity controlled variable of air suspension non-linear rigidity：

According to the air spring nonlinear stiffness characteristic parameter k obtained by being recognized in step (1)_s1And k_s3, and the middle institute of step (3) is really The real-time Optimal Stiffness K of the vehicle air suspension under fixed current running state, the real-time optimal height control to air spring Amount Δ h is designed, i.e.,：

$\mathrm{\&Delta;}h=\sqrt{\frac{K-k_{s1}}{3k_{s3}}}.$